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Assume that the weight of chocolates in boxes of 'celebrations' chocolates in the UK are approximately normally distributed with N(μ=5.8,σ=1.3). Also assume that only those chocolates that weigh between 5 grams and 7 grams can be included for sale in the boxes. State the probability that a randomly chosen chocolate can be included for sale in the celebrations boxes.

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Using the normal distribution principle ; the probability that a randomly chosen chocolate is in the celebration box is 0.553

  • μ=5.8 ; σ=1.3

Zscore = (X - μ) ÷ σ

For X = 5 :

Zscore = (5 - 5.8) ÷ 1.3 = - 0.615

For X = 7 :

Zscore = (7 - 5.8) ÷ 1.3 = 0.923

Using a normal distribution table :

P(Z < 0.923) = 0.822

P(Z < - 0.615) = 0.269

P(Z < 0.923) - P(Z < - 0.615) = 0.822 - 0.269 = 0.553

Therefore, the probability of inclusion is 0.553.

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